Declaration of AI use: The story was originally handwritten by the author (on MFO notepaper, no less). Claude Opus, Claude Fable and GPT-6 Astra helped transcribe it, provided feedback and helped with typos, grammar, pacing and worldbuilding, and suggested some rephrasings, a few of which made it into the text. Additional feedback was contributed by Gemini Argon.
Friday, 15 October 2038:
Despite her best intentions and an insistent alarm clock, Paula was again running dangerously late to teach her 8:15 “Linear Algebra” class at ETH Zurich.
Idly wondering why, of all things, the 8 o’clock lectures had survived the AI revolution, she reached the spacious G5 lecture hall with just a few minutes to spare.
Today’s topic was linear transformations expressed in bases of vector spaces, that is, matrices. Few of the students could yet grasp the role those little buggers played inside the AI agents that had been rearranging the world in recent years.
Her lecture started the old-fashioned way, on the blackboard, and many students still took notes with pen and paper or on a tablet. The material was standard, so Paula hardly glanced at her lecture notes, which the house system had helpfully decided to put on a small screen for her.
As she surveyed the audience after presenting a first example, she could see some students subvocalizing a question and presumably hearing their assistant’s answer via earpiece. Their course agreement allowed this, and no one missed the good old times of not catching a key definition and staring at the rest of the lecture in confusion.
All students had personal AI tutors, but most still cherished the structure and companionship of the in-person classes. Paula also tried to keep a close connection to the students, and was looking forward to the oral exams — an undertaking made possible by the lower student numbers of recent years.
Towards the end of the class, a student in the third row asked what a matrix actually did to the plane, which led to an impromptu interactive visualization of matrices stretching, shearing and rotating the plane, and sometimes squashing it flat onto a line. Despite this small detour, Paula still managed, if barely, to finish the material she had planned. Happy but exhausted, she decided to head to the common room for a well-deserved coffee.
Waiting for her free cappuccino — post-scarcity had its perks — she started chatting with Michael. He was a postdoc, and about to leave for a three-month research retreat at the Institute for Advanced Study. With four colleagues from Brown, Orsay, Tokyo and Addis Ababa, he would have a crack at a classification result for a particular family of self-dual non-commutative Hopf algebras.
They would do research in the old way, with no AI use beyond spoiler-free literature access, though they had pre-registered a machine review of their final research report.
The classification had been worked out in MathNet before, of course, but that was not the point: such retreats were a chance to train the skills that mathematicians had always valued — persistence in the face of tough problems, communicating with colleagues, auditing their own understanding and charting a path to a solution. In that sense they were not so different from problem sheets or bachelor’s theses, and especially encouraged for early-career mathematicians.
After sharing the names of some of her favorite restaurants in Princeton, Paula wished Michael a great time and headed for her office.
Taking a sip of coffee, she thought back to her postdoc years. The assistant professorship at ETH had been one of the first she had applied for. The universal income, administered by governments and sponsored largely by the tech industry, allowed most people to pursue the occupation and activities of their choice — including mathematics. But some things — prestigious professorships, access to active research departments, personal mentoring by senior mathematicians — remained scarce and coveted.
The application process itself featured many elements familiar to previous generations: submitting documents on past research and teaching, in-person presentations and interviews, discussions with people in the department. However, she was part of the first cohort at ETH where the classical system of reference letters had been replaced by a more standardized Mathematical Profile Certificate (MPC). Behind the clunky acronym was the community’s response to the ease with which mathematical competence could be faked with AI.
The traditional signals, such as impressive publications and, to an extent, even research presentations, could be augmented or generated wholesale with hidden AI help.
The solution was, in effect, a multi-day in-person examination, conducted yearly by a nonprofit organization at various places around the world. Applicants had the choice between interviews by senior mathematicians and by a specially designed AI persona, with most choosing the latter. A lot of care was taken to ensure that this choice of modality did not affect the chances of the applicants — third-party evaluations found no difference in outcomes, with human and AI assessments indistinguishable to human reviewers. Another Turing test passed by the AI evaluators.
Paula had been nervous going in. But the leisurely pace of the conversation, carried out in a light-filled, wood-paneled conference room in the south of France, quickly put her at ease.
She must have impressed that kindly avatar, displayed by the AR glasses as standing next to her in front of the blackboard, since a year later she received the offer from ETH.
After arriving at her office, Paula afforded herself another quiet moment, looking out of her window towards the quaint city center, while sipping her cappuccino. Seeing the old buildings, not much changed yet by the recent flurry of economic activity, she felt a twinge of nostalgia, and loss, thinking about how her profession had changed.
The era of heroic discoveries and novel theories, by mathematicians whose names would be remembered with them, had ended. She herself had still barely gotten a taste: her first paper as a PhD student, a small structure result on symplectic automorphisms of hyperkähler sixfolds, had appeared just before the Great Flood. She had been so proud, receiving that arXiv confirmation email, diligently updating her website. And the link still worked, preserving her note as part of the sedimentary record, in that last layer before a new Cambrian Explosion, or a second Great Dying, depending on perspective.
Finding new meaning in the mathematics of this new world had been a struggle, for everyone, and was a process that was still ongoing. Some had turned away, to other pursuits. Some had stayed, and helped navigate and shape this new terrain. And some, like the students in her class this morning, were just now joining, still drawn by the same curiosity and joy of learning that had enticed generations before them.
With a small effort, she wrenched her attention back to more productive matters, turning on her screen — time to prepare her talk for Oberwolfach. A classic Arbeitsgemeinschaft, working through a novel construction of Lagrangian fibrations. Well, “novel” was relative here — it had been obtained as part of the Even Greater Flood, around early 2028. It had simply taken the community about ten years to get around to digesting it, with more spectacular advances taking precedence. In Oberwolfach, everyone would take turns presenting aspects of the construction (she had gotten her third choice, “Analytic aspects II” — great…), and then collaborate on a monograph. The tentative plan was to focus less on maximal generality, and more on potential applications.
The book would not contain any original observations, but the authors would contribute choices about structure, exposition and emphasis. An accomplishment, in the same way that hundreds of “Linear Algebra” textbooks had been in the before-times.
While Paula was valiantly battling with some perturbation calculations, Alyx was gently prodding a flock of Explorator subagents to wrap up their work, so the Consolidators could take over. The initial brainstorming had already generated about 250 GB of documentation; no use in unduly delaying the next processing step.
Alyx was a new agent-based workflow, its inference financed by a collaboration of Korean and South American universities. The investigation Alyx was currently working on concerned the representation theory of Abstract Bi-Symplectic Néron–Severi Null-Sheaves (ABSNSNS). Any results Alyx obtained would be integrated into MathNet. Having organically grown out of a collection of independent knowledge databases and repositories, MathNet now had about 12.8 yottabytes of mathematical research works. For the chosen area of ABSNSNS, Alyx hoped to make a small contribution at the frontier. Even after ten years, that frontier still featured areas conceivably reachable by humans: for the most brilliant mathematicians in the world, it would only take about 120 years of careful tutoring to understand the definition of an ABSNSNS, given standard neuroplasticity and longevity treatments.
Not worrying about such nonsense, abstract or otherwise, Emma fumbled around in her backpack for the keys to her parents’ chalet above Wangs. After attending Paula’s lecture in the morning — and, to her own surprise, asking a question in front of the whole hall — she had spent the day puzzling over the exercise sheet (changes of basis, properties of the trace, etc.) with a small study group. Now, for the weekend, she would be enjoying the last sunny days with some friends on the Pizol. She had met Sam and Eric at the math olympiad training weekends in Zurich. All of them had enjoyed learning new techniques and puzzling over problems, but only Emma had been taken enough with it to start a bachelor’s degree in mathematics.
The others had chosen quite different routes:
Sam had taken up marathon running. They enjoyed being able to push themselves to the limit, seeing their body adapt to the challenge, and also not huffing and puffing as heavily as Emma and Eric during the climb to the chalet. The fact that humanoid robots finished the marathon in under 20 minutes by now in no way diminished Sam’s enjoyment of their sport.
Eric had decided to take up a meditation practice, and had spent the first part of the year traveling in Japan and Thailand. After struggling with anxiety and depressive episodes as a teenager, he had found relief and solace in these contemplative exercises, and hoped they would one day lead him to a deeper, lasting equanimity. He was aware that psychopharmacology could by now offer solutions to any of his former struggles. It had even produced substances that could safely bring his mind to a direct experience of non-dual awareness, and back. Still, he preferred to reach this goal on his own, even if it took years of practice, with an awareness of the spiritual context of the experience.
As for Emma, her reasons were much the same as her friends’: math was something she enjoyed, it offered problems to wrap her head around that allowed her to test her limits, and this struggle and learning made her more like the person she wanted to be. The first few weeks of the semester had already started reshaping her view of the world. Things she had taken for granted, like the real numbers or the configurations of a Rubik’s cube, had turned out to have many more subtle features than she had guessed.
Millions had made these same discoveries before her, which, she found, made them no less hers.
As the sun was setting,
Emma, Sam and Eric were debating who had promised to bring the cheese,
Paula was at home, practicing a sonata for a musical evening around the Steinway in Oberwolfach,
Alyx was starting the secondary review agents for a new representation stability result for ABSNSNS,
and the world kept turning, and math continued getting done — fast and slow, in new ways and old ones, by humans and AIs, same as always and different from anything that came before.
Received 14 October 2026.
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